Sorry for the very long opening post but hopefully it will be helpful!
I would like to qualify some of the comments on this thread. I was raised as a Jehovah's Witness and have been a baptised, active member for almost 30 years. I currently attend meetings but have been mentally out of the religion for some time now. I no longer believe the failed predictions and interpretation of the Bible as presented by Jehovah's Witnesses.
Firstly - to address the concern of the OP. It's your choice whether you think the Watchtower and Awake! magazines are appropriate for the people under your care. TBH, they are pretty tame nowadays, in terms of message, especially the Awake! magazine which is very general interest.
The people leaving the magazines are simply trying to find all avenues to reach people. They are not specifically targeting individuals but would be more than happy to speak to anyone, staff or resident, that might wish to speak to them.
Recent years have seen initiatives to find more people other than those simply behind doors in residential streets hence they have looked at care homes, shops, businesses, fuel stations and, most recently, the mobile trolleys that grace many a town centre these days. Your residence is simply another opportunity.
They will believe that their message of "the good news of Christ's Kingdom" will have relevance to the people at the residence and will expect that, at the very least, the hope presented by a future paradise earth full of perfect people is something that anyone would want to look forward to.
They have zero training in dealing with any sort of vulnerable person whether it be those with mental health care issues, dependencies issues or those in vulnerable social situations.
Whilst not targeting individuals or specific segments of society, there is the potential for a perfect storm of misguided opportunity seeking with a vulnerable person finding a group that seems loving, honest, caring and inclusive (relatively speaking) along with a message that offers a panacea that goes ways beyond the immediate practical help that one might need.
Having said you will probably find that the people that visit will be happy just to leave magazines and go on their way, especially if access to residents is not straight-forward.
Witnesses count the time spent and "placements" of magazines. It's a major part of how a Witness' commitment and spirituality is measured so making those numbers look good at the end of the month is critical.
"Pioneers" are Witnesses who have made a special commitment to spend a certain amount of time proselytising or "witnessing". You can commit to 30 hours a month on a casual basis or 70 hours on a month by month basis.
On a day to day basis most Witnesses are nice people and their religious views are not a major issue.
What happens, however, is that there will be a point where the religious views clash with what would be typical and normal behaviour for most other people.